## 电气工程代写|数字电路代写digital circuit代考|ECEN6003

statistics-lab™ 为您的留学生涯保驾护航 在代写数字电路digital circuit方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写数字电路digital circuit代写方面经验极为丰富，各种代写数字电路digital circuit相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 电气工程代写|数字电路代写digital circuit代考|INVERTING AMPLIFIER

The inverting amplifier configuration shown in Figure $1.11$ amplifies and inverts the input signal in the linear region of operation. The circuit consists of a resistor $R_S$ in series with the voltage source $v_i$ connected to the inverting input of the OpAmp. The non-inverting input of the OpAmp is short circuited to ground (common). A resistor $R_f$ is connected to the output and provides a negative feedback path to the inverting input terminal. ${ }^{12}$ Because the output resistance of the OpAmp is nearly zero, the output voltage $v_o$ will not depend on the current that might be supplied to a load resistor connected between the output and ground.

For most OpAmps, it is appropriate to assume that their characteristics are approximated closely by the ideal OpAmp model of Section 1.2. Therefore, analysis of the inverting amplifier can proceed using the voltage and current constraints of Equations ( $1.5 \mathrm{a})$ and ( $1.5 \mathrm{~b})$,

Node 1 is said to be a virtual ground due to the virtual short circuit between the inverting and non-inverting terminals (which is grounded) as defined by the voltage constraint,
$$v_1=v_2=0 .$$
The node voltage method of analysis is applied at node 1 ,
$$0=\frac{v_i-v_1}{R_S}+\frac{v_0-v_1}{R_f}+i_1 .$$
By applying Equation (1.25), obtained from the virtual short circuit, and the constraint on the current $i_1$ as defined in Equation (1.5b), Equation (1.26) is simplified to
$$0=\frac{v_i}{R_S}+\frac{v_o}{R_f} .$$
Solving for the voltage gain, $v_o / v_i$,
$$\frac{v_o}{v_i}=-\frac{R_f}{R_S}$$
Notice that the voltage gain is dependent only on the ratio of the resistors external to the OpAmp, $R_f$ and $R_S$. The amplifier increases the amplitude of the input signal by this ratio. The negative sign in the voltage gain indicates an inversion in the signal.
The output voltage is also constrained by the supply voltages $V_{C C}$ and $-V_{C C}$,
$$\left|v_o\right|<V_{C C} \text {. }$$
Using Equation (1.28), the maximum resistor ratio $R_f / R_s$ for a given input voltage $v_i$ is
$$\frac{R_f}{R_S}<\left|\frac{V_{C C}}{v_i}\right| .$$

## 电气工程代写|数字电路代写digital circuit代考|NON-INVERTING AMPLIFIER

A non-inverting amplifier is shown in Figure $1.15$ where the source is represented by $v_S$ and a series resistance $R_S$.

The analysis of the non-inverting amplifier in Figure $1.15$ assumes an ideal OpAmp operating within its linear region. The voltage and current constraints at the input to the OpAmp yield the voltage at node 1 ,
$$v_1=v_2=v_s,$$

since $i_1=i_2=0$. Using the node voltage method of analysis, the sum of the currents flowing into node 1 is,
$$0=\frac{0-v_1}{R_G}+\frac{v_o-v_1}{R_f} .$$
Solving for the output voltage $v_o$ using the voltage constraints, $v_1=v_S$
$$v_o=v_i\left(1+\frac{R_f}{R_G}\right) .$$
The gain of the non-inverting amplifier is,
$$\frac{v_o}{v_i}=1+\frac{R_f}{R_G} .$$
Unlike the inverting amplifier, the non-inverting amplifier gain is positive. Therefore, the output and input signals are ideally in phase. The amplifier will operate in its linear region when,
$$1+\frac{R_f}{R_G}<\left|\frac{V_{C C}}{n_s}\right| .$$
Note that, like the inverting amplifier, the gain is a function of the external resistors $R_f$ and $R_G$.

## 电气工程代写|数字电路代写digital circuit代考|INVERTING AMPLIFIER

$$v_1=v_2=0 .$$

$$0=\frac{v_i-v_1}{R_S}+\frac{v_0-v_1}{R_f}+i_1 .$$

$$0=\frac{v_i}{R_S}+\frac{v_o}{R_f} .$$

$$\frac{v_o}{v_i}=-\frac{R_f}{R_S}$$

$$\left|v_o\right|<V_{C C} .$$

## 电气工程代写|数字电路代写digital circuit代考|NON-INVERTING AMPLIFIER

$$v_1=v_2=v_s,$$

$$0=\frac{0-v_1}{R_G}+\frac{v_o-v_1}{R_f} .$$

$$v_o=v_i\left(1+\frac{R_f}{R_G}\right)$$

$$\frac{v_o}{v_i}=1+\frac{R_f}{R_G} .$$

$$1+\frac{R_f}{R_G}<\left|\frac{V_{C C}}{n_s}\right| .$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 电气工程代写|数字电路代写digital circuit代考|ECET365

statistics-lab™ 为您的留学生涯保驾护航 在代写数字电路digital circuit方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写数字电路digital circuit代写方面经验极为丰富，各种代写数字电路digital circuit相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 电气工程代写|数字电路代写digital circuit代考|MODELING THE OPAMP

Terminal voltages and currents are used to characterize $\mathrm{OpAmp}$ behavior. In order to unify all discussions of $\mathrm{OpAmp}$ circuitry, it is necessary to define appropriate descriptive conventions. All voltages are measured relative to a common reference node (or ground) which is external to the chip as is shown in Figure 1.4. The voltage between the inverting pin and ground is denoted as $v_1$ : the voltage between the non-inverting pin and ground is $v_2$. The output voltage referenced to ground is denoted as $v_o$. Power is typically applied to an $\mathrm{OpAmp}$ in the form of two equalmagnitude supplies, denoted $V_{C C}$ and $-V_{C C}$, which are connected to the $\mathrm{V}^{+}$and $\mathrm{V}^{-}$terminals of the OpAmp, respectively.

The reference current directions are shown in Figure 1.4. The direction of current flow is always into the nodes of the $\mathrm{Op}{\mathrm{p}}$ Amp. The current into the inverting input terminal is $i_1$; current into the non-inverting input terminal is $i_2$; current into the output terminal is $i_o$; and the currents into the positive and negative power supply terminals are $I{C-}$ and $I_{C+}$, respectively.

The voltage and current constraints inherent to the input and output terminals of an OpAmp must be understood prior to connecting external circuit elements. The OpAmp is considered as a building block element with specific rules of operation. A short discussion of these rules of operation follows.
The terminal voltages are constrained by the following relationships ${ }^5$
$$v_o=A\left(v_2-v_1\right)$$
and
$$-V_{C C} \leq v_o \leq V_{C C} \text {. }$$
The first of the two voltage constraints states that the output voltage is proportional to the difference between the non-inverting and inverting terminal inputs, $v_2$ and $v_1$, respectively.

## 电气工程代写|数字电路代写digital circuit代考|OPERATIONAL AMPLIFIERS AND APPLICATIONS

Substituting Equations (1.17) and (1.18) into (1.16) yields
$$i_t=\frac{v_t-A i_t R_i}{R_i+R_o} .$$
The Thévenin input resistance, $R_{\text {in }}$, is found by rearranging Equation (1.19),
$$R_{i n}=\frac{v_t}{i_t}=R_i(1+A)+R_o .$$
For the given typical parameter values $\left(R_i=2 \mathrm{M} \Omega, A=200 \mathrm{~K}\right.$, and $\left.R_o=75 \Omega\right)$, the input resistance can be calculated to be the very large value: $R_{i n}=400 \times 10^9 \Omega$. It is reasonable to assume that the input resistance of a unity gain buffer, $R_{i n}$ is, for all practical purposes, infinite.
Example 1.1
Determine the output resistance of an OpAmp voltage follower.
Solution:
To find the output resistance, $R_{\text {out }}$, a test voltage source is connected to the output of the voltage follower to find the Thévenin equivalent resistance at the output. Note also that all independent sources must be zeroed. That is, all independent voltage sources are short circuited and all independent currents are open circuited. The circuit used to find $R_{\text {out }}$ is shown in Figure $1.10 .{ }^{10}$ To find the Thévenin equivalent output resistance, a test voltage source, $v_t$ is connected at the output. The circuit draws $i_t$ source current. The input at $v_2$ has been short circuited to ground to set independent sources to zero.

## 电气工程代写|数字电路代写digital circuit代考|MODELING THE OPAMP

$$v_o=A\left(v_2-v_1\right)$$

$$-V_{C C} \leq v_o \leq V_{C C}$$

## 电气工程代写|数字电路代写digital circuit代考|OPERATIONAL AMPLIFIERS AND APPLICATIONS

$$i_t=\frac{v_t-A i_t R_i}{R_i+R_o} .$$
Thévenin 输入电阻， $R_{\text {in }}$ ，通过重新排列方程 (1.19) 得到，
$$R_{i n}=\frac{v_t}{i_t}=R_i(1+A)+R_o .$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 电气工程代写|数字电路代写digital circuit代考|PHS205

statistics-lab™ 为您的留学生涯保驾护航 在代写数字电路digital circuit方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写数字电路digital circuit代写方面经验极为丰富，各种代写数字电路digital circuit相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 电气工程代写|数字电路代写digital circuit代考|Operational Amplifiers and Applications

The Operational Amplifier (commonly referred to as the OpAmp) is one of the primary active devices used to design low and intermediate frequency analog electronic circuitry: its importance is surpassed only by the transistor. OpAmps have gained wide acceptance as electronic building blocks that are useful, predictable, and economical. Understanding OpAmp operation is fundamental to the study of electronics.

The name, operational amplifier, is derived from the ease with which this fundamental building block can be configured, with the addition of minimal external circuitry, to perform a wide variety of linear and non-linear circuit functions. Originally implemented with vacuum tubes and now as small, transistorized integrated circuits, OpAmps can be found in applications such as: signal processors (filters, limiters, synthesizers, etc.), communication circuits (oscillators, modulators, demodulators, phase-locked loops, etc.), Analog/Digital converters (both A to D and $\mathrm{D}$ to $\mathrm{A}$ ), and circuitry performing a variety of mathematical operations (multipliers, dividers, adders, etc.).

The study of OpAmps as circuit building blocks is an excellent starting point in the study of electronics. The art of electronics circuit and system design and analysis is founded on circuit realizations created by interfacing building block elements that have specific terminal characteristics. OpAmps, with near-ideal behavior and electrically good interconnection properties, are relatively simple to describe as circuit building blocks.

Circuit building blocks, such as the $\mathrm{O}_{\mathrm{p} A} \mathrm{mp}$, are primarily described by their terminal characteristics. Often this level of modeling complexity is sufficient and appropriately uncomplicated for electronic circuit design and analysis. However, it is often necessary to increase the complexity of the model to simplify the analysis and design procedures. These models are constructed from basic circuit elements so that they match the terminal characteristics of the device. Resistors, capacitors, and voltage and current sources are the most common elements used to create such a model: an OpAmp can be described at a basic level with two resistors and a voltage-controlled voltage source.

OpAmp circuit analysis also offers a good review of fundamental circuit analysis techniques. From this solid foundation, the huilding block concept is explored and expanded throughout this text. With the building block concept, all active devices are treated as functional blocks with specified input and output characteristics derived from the device terminal behavior. Circuit design is the process of interconnecting active building blocks with passive components to produce a wide variety of desired electronic functions.

## 电气工程代写|数字电路代写digital circuit代考|BASIC AMPLIFIER CHARACTERISTICS

One of the fundamental characteristics of an amplifier is its gain. ${ }^1$ Gain is defined as the factor that relates the output to the input signal intensities. As shown in Figure 1.1, a time dependent input signal, $x(t)$, is introduced to the “black box” which represents an amplifier and another time dependent signal, $y(t)$, appears at the output.
Figure 1.1: “Black box” representation of an amplifier with input $\mathbf{x}(t)$ and output $\mathbf{y}(t)$.
In actuality, $\mathbf{x}(t)$ can represent either a time dependent or time independent signal. The output of a good amplifier, $\mathbf{y}(t)$, is of the same functional form as the input with two significant differences: the magnitude of the output is scaled by a constant factor, $A$, and the output is delayed by a time, $t_d$. This input-output relationship can be expressed as:
$$\mathbf{y}(t)=A \mathbf{x}\left(t-t_d\right)+\alpha$$
Where
$A$ is the gain of the amplifier,
$\alpha$ is the output DC offset, and
$t_d$ is the time delay between the input and output signals.
The signal is “amplificd” by a factor of $A$. Amplification is a ratio of output signal level to the input signal level. The output signal is amplified when $|A|$ is greater than 1 . For $|A|$ less than 1 , the output signal is said to be attenuated. If $A$ is a negative value, the amplifier is said to invert the input. Should $x(t)$ be sinusoidal, inversion of a signal is equivalent to a phase shift of $180^{\circ}$ : negative $A$ implies the output signal is $\pm 180^{\circ}$ out of phase with the input signal.

For time-varying signals, it may be convenient to find the amplification (ratio) by comparing either the root-mean-squared (RMS) values or the peak values of the input and output signals. Good measurement technique dictates that amplification is found by measuring the input and output RMS values since peak values may, in many instances, be ambiguous and difficult to quantify. ${ }^2$ Unfortunately, in many practical instances, RMS or power meters are not available dictating the measurement of peak amplitudes. The delay time is an important quantity that is often overlooked in electronic circuit analysis and design. ${ }^3$ The signal encounters delay between the input and output of an amplifier simply because it must propagate through a number of the internal components of the amplifying block.

## 电气工程代写|数字电路代写digital circuit代考|Operational Amplifiers and Applications

OpAmp 电路分析还对基本电路分析技术进行了很好的回顾。在这个坚实的基础上，整个文本都探索和扩展了汇丁块的概念。使用构建块概念，所有有源设备都被视为具有从设备终端行为派生的指定输入和输出特征的功能块。电路设计是将有源构建块与无源元件互连以产生各种所需电子功能的过程。

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。